The Pythagorean Kepler

Kepler was on the cusp of the bifurcation
from ancient to modern. In fact, Arthur
Koestler's biography of Kepler is called
The Watershed. This site is devoted
to Kepler's actual watershed,
and has been created by
Ralph Abraham,
and maintained by the
Visual Math Institute.

Kepler's version of the ancient Pythagorean
idea of music broadcast by the crystalline
spheres of the planets: pitch varies continuously
with angular velocity.
Appeared in Mysterium Cosmographicum,
treated in detail in
Harmonice Mundi.

The golden ratio was known in ancient Egypt, and treated carefully
in Euclid's Elements. The Fibonacci sequence appears
in the work of Leonardo of Pisa, ca 1200 CE. The connection between,
still mysterious today, was apparently discovered by Kepler.